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The occurrence of high temperature superconductivity, and the competitionwith magnetism, in stoichiometric and doped LaOFeAs and isostructuraliron-oxypnictides is raising many fundamental questions about the electronicstructure and magnetic interactions in this class of materials. There are nowsufficient experimental data that it may be possible to identify the importantissues whose resolution will lead to the understanding of this system. In thispaper we address a number of the important issues. One important characteristicis the Fe-As distance (or more abstractly the pnictogen (Pn) height $z$(Pn));we present results for the effect of $z$(Pn) on the electronic structure,energetics, and Fe magnetic moment. We also study LaOFeAs under pressure, andinvestigate the effects of both electron and hole doping within the virtualcrystal approximation. The electric field gradients for all atoms in theLaOFeAs compound are presented (undoped and doped) and compared with availabledata. The observed $(\pi,\pi,\pi)$ magnetic order is studied and compared withthe computationally simpler $(\pi,\pi,0)$ order which is probably a very goodmodel in most respects. We investigate the crucial role of the pnictogen atomin this class, and predict the structures and properties of the N and Sbcounterparts that have not yet been reported experimentally. At a certainvolume a gap opens at the Fermi level in LaOFeN, separating bonding fromantibonding bands and suggesting directions for a better simple understandingof the seemingly intricate electronic structure of this system. Finally, weaddress briefly on the possible effects of post-lanthanum rare earths, whichhave been observed to enhance the superconducting critical temperaturesubstantially.

The Delicate Electronic and Magnetic Structure of the LaOFePn System (Pn = pnictogen)